External clock synchronization and sbsolute motion

The “external” clock synchronization goes as follows: Consider that the clocks C(x) located at the points M(x) of the OX axis of I inertial reference frame read all zero (t=0) as a result of a standard (Einstein) clock synchronization procedure. Let C’ be the wrist watch of an observer R’ who moves with constant speed V in the positive direction of the OX axis. Clock C’ is adjusted to read t’=0 when it passes in front of a clock C(x) reading zero as well. The trip of clock C’ lasts dt’ when measured by R’ being a proper time interval but lasts dt when measured by observers from I being a coordinate time interval. The two time intervals are related by the time dilation formula
dt’=dt/g (1)
g representing the Lorentz factor.
Equation (1) enables R’ to find out his speed knowing dt and dt’.
Knowing that the relativity principle could be stated as:
“All physical laws are the same in any inertial reference frame, no inertial reference frame is privileged i.e. distinguishable from the others by means of “internal” empirical evidences” we could say that (1) is an experiment in which the moving observer R’ is not “confined” in his rest frame and so it is out of the requirements of the relativity principle. The way in which the reference frames are chosen is arbitrary.
Is there some error above?

The clocks in the two frames have been synchronised in two different ways.

The C clocks are synchronised by an "internal" method (Einstein sync) which can be carried out in a "closed box" without knowledge of any other frames.

The C' clocks have been synchronised by an "external" method which depends on knowledge of the C clocks.

As the two coordinate systems have been set up in different ways, there's no reason why the laws of physics should take the same mathematical form in the two coordinate systems. The principle of relativity has not been broken because the two observers are not using the same method to make their calculations.

And it's not surprising that R' can work out his velocity relative to I because he made use of I to sync his clocks.

The two time intervals are related by the time dilation formula
dt’=dt/g (1)
g representing the Lorentz factor.
Equation (1) enables R’ to find out his speed knowing dt and dt’.
…
we could say that (1) is an experiment in which the moving observer R’ is not “confined” in his rest frame and so it is out of the requirements of the relativity principle. The way in which the reference frames are chosen is arbitrary.
Is there some error above?

Hi bernhard!

(1) is correct for the time dilation formula for C´ viewed by C, but you cannot use the same process to get the time dilation formula for C viewed by C´, because, as Vanadium 50 says …

Staff: Mentor

Re: "External" clock synchronization and sbsolute motion

However, bernhard is correct. If instead of a single wrist-watch worn by R' we used a system of clocks and rods at rest wrt R', and if those clocks were all synchronized by using the approach bernhard suggests for R', then those rods and clocks would form a new coordinate system I'. In this new coordinate system the formula (1) could indeed be used to calculate coordinate time dilation, however the laws of physics would not take their standard form in this coordinate system as, e.g. the one-way speed of light would be anisotropic.

I don't understand why bernhard would want to construct such a coordinate system, but he could.

The clocks in the two frames have been synchronised in two different ways.

The C clocks are synchronised by an "internal" method (Einstein sync) which can be carried out in a "closed box" without knowledge of any other frames.

The C' clocks have been synchronised by an "external" method which depends on knowledge of the C clocks.

As the two coordinate systems have been set up in different ways, there's no reason why the laws of physics should take the same mathematical form in the two coordinate systems. The principle of relativity has not been broken because the two observers are not using the same method to make their calculations.

And it's not surprising that R' can work out his velocity relative to I because he made use of I to sync his clocks.

However, bernhard is correct. If instead of a single wrist-watch worn by R' we used a system of clocks and rods at rest wrt R', and if those clocks were all synchronized by using the approach bernhard suggests for R', then those rods and clocks would form a new coordinate system I'. In this new coordinate system the formula (1) could indeed be used to calculate coordinate time dilation, however the laws of physics would not take their standard form in this coordinate system as, e.g. the one-way speed of light would be anisotropic.

I don't understand why bernhard would want to construct such a coordinate system, but he could.

Thank you for your help. The approach is not my invention. Tangherlini, Selleri, Edwards and probably many others add to

t=t'/g (1)
a consequence of time dilation
the equation
x'=g(x-Vt) (2)
a consequence of length contraction.
For me the approach has a high pedagogical value,illustrating the difference between experiment performed confined in in an inertial reference frame and experiment performed having an outlook to an experiment performed in an other one.

Staff: Mentor

For me the approach has a high pedagogical value,illustrating the difference between experiment performed confined in in an inertial reference frame and experiment performed having an outlook to an experiment performed in an other one.

I think it would just confuse students. A student could not use such a coordinate system to describe any experiment since the laws of physics (in that coordinate system) would be different from what they had learned.

I think it would just confuse students. A student could not use such a coordinate system to describe any experiment since the laws of physics (in that coordinate system) would be different from what they had learned.

The experiment which leads to t=t'/g does not involve transformation equations at all. It shows only that it is an experiment with outlook to another reference frame enable the moving observer to measure its own speed.
The transformation equations have a large coverage in the literature of the subject.